Question
Find the side $ a $ of a rectangle if side $b = 10\, \text{cm}$ and diagonal $d = 8\, \text{cm}$.
Answer
Problem has no solutions.
Explanation
To find side $ a $ use Pythagorean Theorem:
$$ a^2 + b^2 = d^2 $$After substituting $b = 10\, \text{cm}$ and $d = 8\, \text{cm}$ we have:
$$ a ^ {\,2} + \left( 10\, \text{cm} \right)^{2} = \left( 8\, \text{cm} \right)^{2} $$ $$ a ^ {\,2} = \left( 8\, \text{cm} \right)^{2} - \left( 10\, \text{cm} \right)^{2} $$ $$ a ^ {\,2} = 64\, \text{cm}^2 - 100\, \text{cm}^2 $$ $$ a ^ {\,2} = -36\, \text{cm}^2 $$This equation has no solution $ \Longrightarrow $ The problem has no solution.
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